Solve for x
x\in \left(-\frac{3}{2},3\right)
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2x+3<0 3-x<0
For the product to be positive, 2x+3 and 3-x have to be both negative or both positive. Consider the case when 2x+3 and 3-x are both negative.
x\in \emptyset
This is false for any x.
3-x>0 2x+3>0
Consider the case when 2x+3 and 3-x are both positive.
x\in \left(-\frac{3}{2},3\right)
The solution satisfying both inequalities is x\in \left(-\frac{3}{2},3\right).
x\in \left(-\frac{3}{2},3\right)
The final solution is the union of the obtained solutions.
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